Theme Essential Question: How can you analyze proportional relationships and use them to solve real-world and mathematical problems?
Essential Questions: How can you rewrite expressions to help you solve problems?
Standards:
7.RP.3 Analyze proportional relationships and use them to solve real-world and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems.
7. EE.2 Use properties of operations to generate equivalent expressions. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”
Objectives:
The student will explain the rational and generate expressions to calculate markups and markdowns by adding ±1 to the percentage.
The student will understand and apply the strategy of rewriting an expression in different forms in a problem context in order to shed light on the problem and how the quantities in it are related.
Provide students the opportunity to complete their portfolios. Students should present and/or display their work.
Key Questions
How can rewriting expressions help you set up problems and facilitate their solutions?
When you multiply by a number greater than one, is the product more or less than the original number?
Observable Student Behaviors
Observation of student’s participation and products
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
See other lesson in this unit
Suggested Activities:
Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 3-2, p. 63-64
ABC Mastering the Common Core in Mathematics
Changing Algebra Word Problems to Algebraic Equations, Chapter 8.5, p. 96
Chapter 8 Review and Test, p. 97-98
Gizmo Lessons
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations.
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.
Teaching the Common Core Math Standards with Hands-On Activities,
7.PR.3 – Activity p.86
Highly Recommended (Use this time to complete prior problems)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels. Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.
Students play a generalized version of connect four, gaining the chance to place a piece on the board by answering arithmetic questions (addition, subtraction, multiplication, division). Parameters: time, difficulty level, types of questions. Arithmetic Four is one of the Interactivate assessment games.
Related Topics: addition, arithmetic, assessment, division, integers, multiplication, negative number, positive number, positive part of the operand, subtraction, whole numbers
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Grade: 7 Unit: 3 Week: 5 Dates: 12/10 – 12/14
Content: Rewriting Expressions
Theme Essential Question:
How can you analyze proportional relationships and use them to solve real-world and mathematical problems?
Essential Questions:
How can you rewrite expressions to help you solve problems?
Standards:
Objectives:
Background Information
Assessment:
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Suggested Activities:- Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 3-2, p. 63-64
- ABC Mastering the Common Core in Mathematics
- Changing Algebra Word Problems to Algebraic Equations, Chapter 8.5, p. 96
- Chapter 8 Review and Test, p. 97-98
- Gizmo Lessons
- Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations.- Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.- Teaching the Common Core Math Standards with Hands-On Activities,
- 7.PR.3 – Activity p.86
- Highly Recommended (Use this time to complete prior problems)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Diverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Measurement and children’s Literature/Ratios
http://sci.tamucc.edu/~eyoung/measure_literature.html- Mathematics in Children's Literature:
Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels. Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
Videos
- Discovery Learning http://www.discoveryeducation.com/
- The Teaching Channel
- The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
https://www.teachingchannel.org/videos?categories=topics common-coreSMART Board Lessons, Promethean Lessons
Other Activities, etc.
Language
Arts
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Matrix
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